Question

How do you factor #y= 2x^3-2x^2-4x #?

Answer 1

`y = 2x^3-2x^2-4x = 2x(x+1)(x-2)`

Explanation:

First note that all of the terms are divisible by `2x`, so separate that out as a factor:

`y = 2x^3-2x^2-4x = 2x(x^2-x-2)`

Then notice that if you substitute `x=-1` into `x^2-x-2`, the result is `0`, so `(x+1)` is a factor and the other factor must be `(x-2)` to get the `-2` constant term when multiplied:

`(x^2-x-2) = (x+1)(x-2)`

So we have:

`y = 2x^3-2x^2-4x = 2x(x+1)(x-2)`